Generalized Speedy Q-Learning

Speedy Q-Learning

We introduce a new convergent variant of Q-learning, called speedy Q-learning, in order to address the problem of slow convergence in the standard form of the Q-learning algorithm. We prove a PAC bound on the performance of SQL, which shows that only T = O ( log(1/δ)ǫ(1 − γ) ) steps are required for the SQL algorithm to converge to an ǫ-optimal action-value function with high probability. This ...

Speedy Q-Learning: A Computationally Efficient Reinforcement Learning Algorithm with a Near-Optimal Rate of Convergence∗

We consider the problem of model-free reinforcement learning (RL) in the Markovian decision processes (MDP) under the probably approximately correct (PAC) model. We introduce a new variant of Q-learning, called speedy Q-learning (SQL), to address the problem of the slow convergence in the standard Q-learning algorithm, and prove PAC bounds on the performance of this algorithm. The bounds indica...

PRESENTING GENERALIZED q - SCHUR

Generalized Q-functions

The modulus squared of a class of wave functions defined on phase space is used to define a generalized family of Q or Husimi functions. A parameter λ specifies orderings in a mapping from the operator |ψ〉〈σ| to the corresponding phase space wave function, where σ is a given fiducial vector. The choice λ = 0 specifies the Weyl mapping and the Q-function so obtained is the usual one when |σ〉 is ...

GENERALIZED q - FIBONACCI NUMBERS

We introduce two sets of permutations of {1, 2, . . . , n} whose cardinalities are generalized Fibonacci numbers. Then we introduce the generalized q-Fibonacci polynomials and the generalized q-Fibonacci numbers (of first and second kind) by means of the major index statistic on the introduced sets of permutations.